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Let's consider what happens
when we have an object that's

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moving on a horizontal surface.

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So here's our object,
and here's our surface.

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Now, we want to look
at a special case

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where we're applying a
force F to the object,

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and the object is moving
at a constant speed.

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Then what we see
here is that there

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has to be some type
of force that's

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opposing this object, the
interaction between the object

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and the surface, that's
distributed over the surface.

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For this, I'll write an arrow
here to express that force.

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That's the tangential
component of the force.

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The object is also pressing
down on the surface.

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The surface is pressing
up on the object.

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And so there's another
perpendicular force

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to the surface,
which is referred

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to as the normal force.

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And the total vector sum
of these two forces--

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the perpendicular
part, the normal force,

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and the tangential
part-- is referred to

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as the contact force.

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This is what we'll
call kinetic friction.

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Now, when the object is
moving at a constant speed,

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we know that, from experiment,
that the kinetic friction,

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the magnitude, is
proportional to the magnitude

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of the normal force.

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And the constant
of proportionality

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is called the coefficient
of kinetic friction.

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Now, this law is telling us
something very interesting,

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that key properties
are, one, that it's

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independent of the contact area.

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Now, what do we mean by that?

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So let's look at the
following picture.

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Suppose we have two
objects of the same mass.

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On the surface, we're applying
a force F and the contact area

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here, A1.

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And we have a similar
object, the same mass,

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on the same surface.

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And both objects are
moving at a constant speed.

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Now, these objects
have different areas

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of contact, A1 and A2.

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But the force necessary
to move the object

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at the constant
speed is the same.

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And because of that, the
kinetic friction is the same.

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And that indicates that it's
independent of the contact

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area.

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And the other key property here,
which we'll write over here,

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is that it's independent
of the speed of the object.

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So we'll write that as
independent of the velocity.

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And these three properties
of kinetic friction

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are crucial for understanding
the motion of objects

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across a surface.

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But we still don't have a
very good theoretical model

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for explaining this,
although today, there

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is a lot of
contemporary research

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which has made a lot of
progress in understanding

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this interaction.